I'm wondering though there are any advantages of having an app as well as a mobile site. Does anyone have any thoughts?

I just can't come up with a reason to have an app as my view is that a mobile site is more appropriate for attracting new clients whereas an app would only be relevant for existing clients - no one is going to turn to an app to try to locate a massage therapist. I guess it might be a little easier for online booking schedules but that's about all I can come up with.

There are some advantages and disadvantage to have a mobile app at a technical level.

Mobile apps are great to keep existing customers, but they tend to also have less performance issues when running such as not slowing down due to a surge of users accessing the app; however, the issue with them is that you have to create a new mobile app for each type of phone and in order maintain the app you have to hire an outside developer if you yourself don't know how to do it, which can become an expensive endeavor especially if you need to update the app often.

I agree with WhyMassage, if you're only looking for a mobile version of your site. Put your time, effort and/or money on creating a fully responsive web site and it will look good in any unit and Google will like it as well. I think app is the better choice only if you've come up with a product/service that runs with an online software, for example a training diary, meditation guide or similar. The app will be faster, can be used offline, take advantage of build-in UI, and you can earn money.

An app which only purpose is to promote a local business is likely to be rejected by for example Apple, they will see it as only commercial and no value to the user.